Final answer:
To determine the greatest number of identical care packages, the greatest common divisor of 18 and 42 must be found, which is 6. As a result, the greatest number of identical care packages that can be made is six, and each will contain 3 granola bars and 7 pairs of socks.
Step-by-step explanation:
The question is asking what is the greatest number of identical care packages that can be made using all the granola bars and pairs of socks with nothing left over. To find this, we need to determine the greatest common divisor (GCD) of 18 granola bars and 42 pairs of socks, because the GCD will give us the largest number of identical packages that can be made without any leftover items.
To find the GCD of 18 and 42, we can list the factors of each:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
The largest common factor is 6. Therefore, the greatest number of identical care packages that can be made is 6, which makes option a) 6 the correct answer. Each package will contain 3 granola bars (18 divided by 6) and 7 pairs of socks (42 divided by 6).